The relative efficiency of direct and maximum likelihood estimates of mean waiting time in the simple queue, M/M/1

Jenkins, John H.

doi:10.1017/s0021900200095061

Cited by 4 publications

(5 citation statements)

References 2 publications

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“…Jenkins [20] compares the relative efficiencies of the direct estimate for the mean waiting time with that suggested by Clarke, and concludes that the MLE has a lower asymptotic variance, particularly for high values of load ρ, defined as λ µ . Aigner [3] summarises known work at the time (1974) and compares various estimators of different queue parameters for the M/M/1 queue, when the number of packets sampled is fixed.…”

Section: Inference and Estimatorsmentioning

confidence: 99%

Optimal design of measurements on queueing systems

et al. 2014

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We examine the optimal design of measurements on queues with particular reference to the M/M/1 queue. Using the statistical theory of design of experiments, we calculate numerically the Fisher information matrix for an estimator of the arrival rate and the service rate to find optimal times to measure the queue when the number of measurements are limited for both interfering and non-interfering measurements.We prove that in the non-interfering case, the optimal design is equally spaced. For the interfering case, optimal designs are not necessarily equally spaced. We compute optimal designs for a variety of queuing situations and give results obtained under the D-and D s -optimality criteria.

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Section: Inference and Estimatorsmentioning

confidence: 99%

Optimal design of measurements on queueing systems

et al. 2014

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“…For simulation purposes, we set λ = 2.5 s −1 . The reader will note that θ = λ here, that is, we wish to measure one of the simulation parameters, but we do not use knowledge of this λ when estimatingû using (7).…”

Section: Example 1: a Single M/m/1 Queuementioning

confidence: 99%

“…Jenkins [7] compared relative efficiencies of the direct estimate for the mean waiting time with that suggested by Clarke, and concludes that the MLE has a lower asymptotic variance, particularly for high values of load.…”

Section: Related Workmentioning

confidence: 99%

Utility based framework for optimal network measurement

2015

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Packet level measurement is now routinely used to evaluate the loss and delay performance of broadband networks. In active measurement, probe packets provide samples of the loss and delay, and from these samples the performance of the traffic as a whole can be deduced. However this is prone to errors: inaccuracy due to taking insufficient samples, self-interference due to injecting too many probe packets, and possible sample-correlation induced bias. In this paper we consider the optimization of probing rate by treating all measurements as numerical experiments which can be optimally designed by using the statistical principles of Design of Experiments. We develop an analytical technique that quantifies an overall utility function associated with: i) the disruption caused per probe packet, ii) the bias and iii) the variance as a function of the probing (sampling) rate. Our numerical results show that the optimal probing rate depends strongly on what parameter the network engineer seeks to measure.

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“…An interesting approach to estimating the mean sojourn time /lv involving observations on X(t) has been given by Jenkins (1972) He also uses the result that '" 2T fooo y(x)dx for large T provided that y(x) does not converge to zero too slowly as x~00. Also, he shows that…”

Section: Application To Mean Estimationmentioning

confidence: 99%

The covariance structure of queues and related processes – a survey of recent work

Reynolds¹

1975

Advances in Applied Probability

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This paper surveys recent results on the covariance structure of processes generated by queues and related stochastic processes. The generated processes include the number X(t) of customers at time t, the waiting time Wn of the nth customer and the inter-departure interval Dn, i.e., the interval between departures of the nth and (n+1)th customers. The importance of these results is discussed, particularly in the field of estimation.

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The relative efficiency of direct and maximum likelihood estimates of mean waiting time in the simple queue, M/M/1

Cited by 4 publications

References 2 publications

Optimal design of measurements on queueing systems

Optimal design of measurements on queueing systems

Utility based framework for optimal network measurement

The covariance structure of queues and related processes – a survey of recent work

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